Virtualbox support live migration but refers to it as teleportation.

Teleportation is the process of moving a running virtual machine from one physical computer to another. Teleporting between hosts of differing CPUs is not always successful.

To support teleporation, the VMs hard drives must be located on some type of shared storage, "NFS, Windows share or iSCSI", which both computers have concurrent access to. The process of doing the teleporation is done by command line only.

A VM is created on the target computer with the exact same settings as the VM running on the source host including the same hard drives, but with the following modification to cause it to wait for the running state of the source VM to be sent to it.

VBoxManage modifyvm  VMName --teleporter on --teleporterport 12345 --teleporterpassword PassWord

The target VM is started and it listens on the network for a connection from the source VM to transfer the VM state

VBoxManage --startvm VMName

The source VM is commanded to teleport itself to the waiting target VM.

VBoxManage controlvm VMName teleport --host  TargetComputer --port 12345 --password PassWord

TechSologic Infinity with its shared storage architecture supports teleportation with its GUI interface by dragging and dropping a running VM to another host or by changing the VMs Host group in its properties.